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Four Generated, Squarefree, Monomial Ideals

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Bridging Algebra, Geometry, and Topology

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 96))

Abstract

Let I⊋ J be two squarefree monomial ideals of a polynomial algebra over a field generated in degree ≥ d, resp. ≥ d + 1. Suppose that I is either generated by three monomials of degrees d and a set of monomials of degrees ≥ d + 1, or by four special monomials of degrees d. If the Stanley depth of I∕J is ≤ d + 1 then the usual depth of I∕J is ≤ d + 1 too.

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Acknowledgements

The support of the first author from the Department of Mathematics of the University of Kaiserslautern and the support of the second author from grant PN-II-RU-TE-2012-3-0161 of Romanian Ministry of Education, Research and Innovation are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Str., 67663, Kaiserslautern, Germany

    Adrian Popescu

  2. Simion Stoilow Institute of Mathematics of Romanian Academy, Research unit 5, 1-764, Bucharest, 014700, Romania

    Dorin Popescu

Authors
  1. Adrian Popescu
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  2. Dorin Popescu
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Corresponding author

Correspondence to Adrian Popescu .

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Editors and Affiliations

  1. Faculty of Mathematics and Informatics, Ovidius University, Constanta, Constanta, Romania

    Denis Ibadula

  2. Department of Mathematics, University of Leuven, Leuven (Heverlee), Belgium

    Willem Veys

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Popescu, A., Popescu, D. (2014). Four Generated, Squarefree, Monomial Ideals. In: Ibadula, D., Veys, W. (eds) Bridging Algebra, Geometry, and Topology. Springer Proceedings in Mathematics & Statistics, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-09186-0_14

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